The surface area of a figure is the sum of the areas of all its sides. To find the area of the cylinder, you must find the area of the base and add it to the area of the outer wall or blanket. The formula for finding the surface area of a cylinder is L = 2πr2 + 2πrt.
Step
Part 1 of 3: Calculating the Surface Area of the Tube Base (2 x (π x r2))
Step 1. Draw the top and bottom of the tube
Soup cans have a cylindrical shape. If you think about it, the can has the same shape at the top and bottom, which is a circle. The first step to finding the surface area of your cylinder is to find the area of these two circles.
Step 2. Find the radius of your tube
The radius is the distance from the center of the circle to the outside of the circle. The radius is abbreviated as “r”. The radius of the cylinder is equal to the radius of the upper and lower circles. In this example, the radius of the base is 3 cm.
- If you solve story problems, the radius may already be known. The diameter may also be known, i.e. the distance from one side of the circle to the other through the center. The radius is half the diameter.
- You can measure the radius with a ruler if you want to find the actual surface area of the cylinder.
Step 3. Calculate the surface area of the top circle
The surface area of a circle is equal to the constant pi (~3, 14) times the radius of the circle squared. The equation is written as x r2. This is equal to x r x r.
- To find the area of the base, just plug the radius 3 cm into the equation to find the surface area of a circle: L = r2. Here's how to calculate it:
- L = r2
- L = x 32
- L = x 9 = 28, 26 cm2
Step 4. Do the same calculation for the bottom circle
Now that you know the area of one of the bases, you must calculate the area of the second. You can use the same calculation steps as the first base. Or, you may notice that the two bases of these circles are exactly the same. so there is no need to calculate the area of the second base if you understand it.
Part 2 of 3: Calculating the Surface Area of a Tube Blanket (2π x r x t)
Step 1. Draw the outside of a tube
When you imagine a soup can shaped like a tube, you'll see a top and bottom base. The two pedestals are connected by the “wall” of the can. The wall radius is the same as the base radius. However, unlike the plinth, this wall has a height.
Step 2. Find the circumference of one of the circle's bases
You'll need to find the circumference of a circle to find its outer surface area (also called lateral surface area or tube blanket). To find the circumference, just multiply the radius by 2π. So, the perimeter can be found by multiplying 3 cm by 2π, or 3 cm x 2π = 18.84 cm.
Step 3. Multiply the circumference of the circle by the height of the cylinder
This calculation will give the surface area of the tube blanket. Multiply the circumference, 18.84 cm by the height, 5 cm. So, 18.84 cm x 5 cm = 94.2 cm2.
Part 3 of 3: Adding up ((2) x (π x r2)) + (2π x r x h)
Step 1. Imagine a complete tube
First, you imagine the top and bottom bases and find the surface area of both. Next, you imagine a wall that runs between the two bases and find its area. This time, imagine a whole can, and you'll find the total surface area.
Step 2. Multiply the area of one of the bases by two
Just multiply the previous result, 28, 26 cm2 by 2 to get the area of the two bases. So, 28.26 x 2 = 56.52 cm2. This calculation gives the area of the two bases.
Step 3. Add up the area of the blanket and the two bases
After adding up the area of both the base and the cover of the tube, you get the surface area of the cylinder. All you have to do is add up the area of the two bases, which is 56.52 cm2 and the area of the blanket, which is 94.2 cm2. So, 56, 52 cm2 + 94.2 cm2 = 150, 72 cm2. The surface area of a cylinder with a height of 5 cm and the base of a circle with a radius of 3 cm is 150.72 cm2.
Tips
If your height or radius has a square root symbol, see the article Multiplying Square Roots for more information
Warning
Always remember to multiply the area of the base by two to calculate the second base
Related wikiHow Articles
- Calculating the Surface Area of a Cone
- Calculating Cylinder Volume
- Calculating the Surface Area of a Rectangular Prism
- Finding the Surface Area of a Cube
